WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(0, 6) L :: ["A"(0, 6)] -(0)-> "A"(2, 6) L :: ["A"(0, 6)] -(0)-> "A"(0, 6) L :: ["A"(0, 6)] -(0)-> "A"(8, 6) L :: ["A"(0, 6)] -(0)-> "A"(13, 6) L :: ["A"(0, 6)] -(0)-> "A"(12, 6) N :: ["A"(0, 6) x "A"(8, 6)] -(2)-> "A"(2, 6) N :: ["A"(0, 6) x "A"(14, 6)] -(8)-> "A"(8, 6) N :: ["A"(0, 6) x "A"(9, 6)] -(3)-> "A"(3, 6) max :: ["A"(2, 6)] -(4)-> "A"(0, 6) s :: ["A"(0, 6)] -(6)-> "A"(0, 6) s :: ["A"(0, 6)] -(6)-> "A"(2, 6) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1, 0) "0_A" :: [] -(0)-> "A"(0, 1) "L_A" :: ["A"(0, 0)] -(0)-> "A"(1, 0) "L_A" :: ["A"(0, 1)] -(0)-> "A"(0, 1) "N_A" :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(1, 0) "N_A" :: ["A"(0, 1) x "A"(1, 1)] -(0)-> "A"(0, 1) "s_A" :: ["A"(0, 0)] -(0)-> "A"(1, 0) "s_A" :: ["A"(0, 1)] -(1)-> "A"(0, 1) WORST_CASE(?,O(n^2))